Co-evolution in Epistemic Networks Reconstructing Social Complex Systems
Camille Roth CREA – CNRS / Ecole Polytechnique
Presentation of the thesis — Nov 19, 2005
Framework and objectives
Epistemic communities
Micro-foundations
The Reconstruction Problem
Reconstruction is a reverse problem consisting in successfully reproducing several stylized facts observed in the original empirical system.
Framework and objectives
Epistemic communities
Micro-foundations
The Reconstruction Problem Reconstruction is a reverse problem consisting in successfully reproducing several stylized facts observed in the original empirical system. Issues e
(i) Find P in order to deduce high-level observations H from strictly low-level phenomena L. (ii) Find a low-level dynamics λ that rebuilds high-level evolution η e .
Ht
η
Ht+∆t P?
P? e
Lt
λ
L t+∆t
Framework and objectives
Epistemic communities
Micro-foundations
The Reconstruction Problem Reconstruction is a reverse problem consisting in successfully reproducing several stylized facts observed in the original empirical system. Issues e
(i) Find P in order to deduce high-level observations H from strictly low-level phenomena L. (ii) Find a low-level dynamics λ that rebuilds high-level evolution η e .
Ht
η
P
P Lt
Ht+∆t
λ?
L t+∆t
Framework and objectives
Epistemic communities
Micro-foundations
Objectives A socio-semantic complex system 1
Reproduce a hierarchic epistemic hypergraph of a knowledge community that fits a high-level expert-based description
2
Provide a low-level dynamics and a morphogenesis model that rebuilds the empirically observed high-level structure
Thesis The structure of a knowledge community, and in particular its epistemic hypergraph, is primarily produced by the co-evolution of agents and concepts.
Framework and objectives
Epistemic communities
Micro-foundations
Objectives A socio-semantic complex system 1
Reproduce a hierarchic epistemic hypergraph of a knowledge community that fits a high-level expert-based description
2
Provide a low-level dynamics and a morphogenesis model that rebuilds the empirically observed high-level structure
Thesis The structure of a knowledge community, and in particular its epistemic hypergraph, is primarily produced by the co-evolution of agents and concepts.
Framework and objectives
Epistemic communities
Outline
1
Epistemic communities Rationale & definitions Epistemic community taxonomy and Galois lattices Partial taxonomies: rebuilding history
2
Micro-foundations of epistemic networks Networks Towards a rebuilding model Reconstruction of epistemic communities
Micro-foundations
Framework and objectives
Epistemic communities
Outline
1
Epistemic communities Rationale & definitions Epistemic community taxonomy and Galois lattices Partial taxonomies: rebuilding history
2
Micro-foundations of epistemic networks Networks Towards a rebuilding model Reconstruction of epistemic communities
Micro-foundations
Framework and objectives
Epistemic communities
Micro-foundations
Epistemic community taxonomy and Galois lattices
Building taxonomies
Rationale Describe the taxonomy of a knowledge community, in particular scientific communities, that matches high-level descriptions. e
Ht
η
Ht+∆t P
P e
Lt
λ
L t+∆t
Framework and objectives
Epistemic communities
Micro-foundations
Epistemic community taxonomy and Galois lattices
Building taxonomies
Epistemic communities Epistemic Community: group of agents sharing a common set of subjects, concepts, issues; sharing a common goal of knowledge creation — Haas (1992), Cowan et al. (2000) Definition here: “an epistemic community is the largest set of agents sharing a given set of concepts” – as such strongly linked with structural equivalence
Framework and objectives
Epistemic communities
Micro-foundations
Epistemic community taxonomy and Galois lattices
Building taxonomies
Epistemic communities Epistemic Community: group of agents sharing a common set of subjects, concepts, issues; sharing a common goal of knowledge creation — Haas (1992), Cowan et al. (2000) Definition here: “an epistemic community is the largest set of agents sharing a given set of concepts” – as such strongly linked with structural equivalence
Framework and objectives
Epistemic communities
Micro-foundations
Epistemic community taxonomy and Galois lattices
Building taxonomies Formal framework Consider a binary relation R between agents & concepts Intent S ∧ of an agent set S: all concepts used by every agent in S
Concepts (C) Prs
s1
Extent C ? of a concept set C Epistemic community: the extent of a concept set C “∧?” is a closure operation: 1 2 3
(idempotent) (S ∧? )∧? = S ∧? (extensive) S ⊆ S ∧? (increasing) S ⊆ S 0 ⇒ S ∧? ⊆ S 0∧?
(S, C) is closed iff C = S ∧ and S = C ?
Lng
s2 NS
s3 s4
Agents (S)
Framework and objectives
Epistemic communities
Micro-foundations
Epistemic community taxonomy and Galois lattices
Building taxonomies Formal framework Consider a binary relation R between agents & concepts Intent S ∧ of an agent set S: all concepts used by every agent in S
Concepts (C) Prs
s1
Extent C ? of a concept set C Epistemic community: the extent of a concept set C “∧?” is a closure operation: 1 2 3
(idempotent) (S ∧? )∧? = S ∧? (extensive) S ⊆ S ∧? (increasing) S ⊆ S 0 ⇒ S ∧? ⊆ S 0∧?
(S, C) is closed iff C = S ∧ and S = C ?
Lng
s2 NS
s3 s4
Agents (S)
Framework and objectives
Epistemic communities
Micro-foundations
Epistemic community taxonomy and Galois lattices
Building taxonomies Formal framework Consider a binary relation R between agents & concepts Intent S ∧ of an agent set S: all concepts used by every agent in S
Concepts (C) Prs
s1
Extent C ? of a concept set C Epistemic community: the extent of a concept set C “∧?” is a closure operation: 1 2 3
(idempotent) (S ∧? )∧? = S ∧? (extensive) S ⊆ S ∧? (increasing) S ⊆ S 0 ⇒ S ∧? ⊆ S 0∧?
(S, C) is closed iff C = S ∧ and S = C ?
Lng
s2 NS
s3 s4
Agents (S)
Framework and objectives
Epistemic communities
Epistemic community taxonomy and Galois lattices
Building taxonomies
Representing epistemic communities 1
structured into fields, with common concerns,
2
hierarchically: generalization / specialization,
3
overlapping.
From trees to lattices
Micro-foundations
Framework and objectives
Epistemic communities
Micro-foundations
Epistemic community taxonomy and Galois lattices
Building taxonomies
Representing epistemic communities
From trees to lattices mammal
bird platypus
platypus
1
2
3
structured into fields, with common concerns, hierarchically: generalization / specialization, overlapping.
mammal
bird
platypus lattice
tree Italy
Germany
tree Rural Italy
Urban Italy
Territories lattice
Italy Urban Italy
Germany Rural Italy
Urban Germany
Rural Germany
Habitat Urban Urban Germany
Rural Rural Germany
Framework and objectives
Epistemic communities
Epistemic community taxonomy and Galois lattices
Building taxonomies Galois lattices GL={(S ∧? , S)|S ⊆ S} is the partially-ordered set of all epistemic communities, with the partial order: (X , X ∧ ) < (X 0 , X 0∧ ) ⇔ X ⊂ X 0 ( s 1 s 2 s 3s 4 ; ∅ ) ( s 1 s 2 s 3 ; Lng ) (s 1s 2 ; Lng Prs )
GL ( s 2 s 3 s 4 ; NS )
( s 2s 3 ; Lng NS )
( s 2 ; Lng Prs NS )
Micro-foundations
Framework and objectives
Epistemic communities
Micro-foundations
Epistemic community taxonomy and Galois lattices
Managing taxonomies
Taxonomy selection & extraction Which ECs should we extract from the lattice? Given the assumptions, a first criterion is agent set size — Small isolated ECs could be interesting too. In order to create a partial taxonomy, with selection heuristics: partially-ordered set overlaying the lattice: “epistemic hypergraph”
( s 1 s 2 s 3s 4 ; ∅ ) ( s 1 s 2 s 3 ; Lng ) (s 1s 2 ; Lng Prs )
GL ( s 2 s 3 s 4 ; NS )
( s 2s 3 ; Lng NS )
( s 2 ; Lng Prs NS )
poset ( s 1 s 2 s 3s 4 ; ∅ ) ( s 1 s 2 s 3 ; Lng )
( s 2 s 3 s 4 ; NS )
Framework and objectives
Epistemic communities
Micro-foundations
Epistemic community taxonomy and Galois lattices
Managing taxonomies
Taxonomy selection & extraction Which ECs should we extract from the lattice? Given the assumptions, a first criterion is agent set size — Small isolated ECs could be interesting too. In order to create a partial taxonomy, with selection heuristics: partially-ordered set overlaying the lattice: “epistemic hypergraph”
( s 1 s 2 s 3s 4 ; ∅ ) ( s 1 s 2 s 3 ; Lng ) (s 1s 2 ; Lng Prs )
GL ( s 2 s 3 s 4 ; NS )
( s 2s 3 ; Lng NS )
( s 2 ; Lng Prs NS )
poset ( s 1 s 2 s 3s 4 ; ∅ ) ( s 1 s 2 s 3 ; Lng )
( s 2 s 3 s 4 ; NS )
Framework and objectives
Epistemic communities
Micro-foundations
Epistemic community taxonomy and Galois lattices
Managing taxonomies
Taxonomy selection & extraction Which ECs should we extract from the lattice? Given the assumptions, a first criterion is agent set size — Small isolated ECs could be interesting too. In order to create a partial taxonomy, with selection heuristics: partially-ordered set overlaying the lattice: “epistemic hypergraph”
( s 1 s 2 s 3s 4 ; ∅ ) ( s 1 s 2 s 3 ; Lng ) (s 1s 2 ; Lng Prs )
GL ( s 2 s 3 s 4 ; NS )
( s 2s 3 ; Lng NS )
( s 2 ; Lng Prs NS )
poset ( s 1 s 2 s 3s 4 ; ∅ ) ( s 1 s 2 s 3 ; Lng )
( s 2 s 3 s 4 ; NS )
Framework and objectives
Epistemic communities
Micro-foundations
Epistemic community taxonomy and Galois lattices
Managing taxonomies Taxonomy evolution growth
1
Progress or decline of a field
(S1,C)
decrease
merge
2
Merging or scission of a field
(S2 ,C)
(S,C)
(S’,C’)
(S ∩ S’,C ∪ C’)
scission
(S2 ,C)
Framework and objectives
Epistemic communities
Micro-foundations
Partial taxonomies: rebuilding history
Empirical results Hierarchical epistemic hypergraph 1990-1995 All (255)
Dev (168) Hom (67)
Mou (92)
Hum (34)
Brn (102)
Ver (75)
Pat (99) Spi (30)
Ven (50) Dor (49)
Gro (44) Sig (53)
Mou Dev (72) Hom Mou (40)
Dev Brn (81) Mou Hum (18)
Hom Hum (11)
Dev Pat (77) Ver Dev (68) Mou Ver (30)
Ven Dor (34) Brn Pat (62) Ver Pat (42)
Brn Ven (43) Brn Spi Crd (29)
Brn Dor (38)
Brn Ven Dor (30) Brn Spi Crd Ven (15)
Pwy (38)
Framework and objectives
Epistemic communities
Micro-foundations
Partial taxonomies: rebuilding history
Empirical results Hierarchical epistemic hypergraph 1998-2003 All (255)
Dev (150) Hom (57)
Mou (100)
Hum (100)
Brn (82) Ver (86)
Pat (90)
Dev Brn (62)
Mou Hum (58)
Hom Hum (38)
Gro (67)
Sig (133)
Mou Dev (71)
Hum Ver (44) Hom Mou (35)
Ven (40) Dor (40) Spi Crd (18)
Dev Pat (78) Ver Dev (70)
Sig Pwy (84) Gro Sig (51) Ven Dor (24)
Sig Rec (48) Gro Pwy (42)
Pat Brn (47)
Mou Ver (48)
Rec (67) Pwy (93)
Pwy Rec (34)
Ver Pat (58)
Gro Sig Pwy (39) Sig Pwy Rec (31)
Framework and objectives
Epistemic communities
Micro-foundations
Partial taxonomies: rebuilding history
Empirical results
Historical description 1
Research on brain and spinal cord depreciated,
2
The community started to enquire relationships between signal, pathway, and receptors,
3
Mouse-related research is stable, yet significant stress on human-related topics & new relationship to homologous genes and vertebrates: growing focus on differential studies.
Matches expert-based descriptions
Framework and objectives
Epistemic communities
Micro-foundations
Partial taxonomies: rebuilding history
Empirical results
Historical description 1
Research on brain and spinal cord depreciated,
2
The community started to enquire relationships between signal, pathway, and receptors,
3
Mouse-related research is stable, yet significant stress on human-related topics & new relationship to homologous genes and vertebrates: growing focus on differential studies.
Matches expert-based descriptions
Framework and objectives
Epistemic communities
Outline
1
Epistemic communities Rationale & definitions Epistemic community taxonomy and Galois lattices Partial taxonomies: rebuilding history
2
Micro-foundations of epistemic networks Networks Towards a rebuilding model Reconstruction of epistemic communities
Micro-foundations
Framework and objectives
Epistemic communities
Networks
Overview
e
Ht
η
Ht+∆t P
P e
Lt
λ
L t+∆t
Micro-foundations
Framework and objectives
Epistemic communities
Micro-foundations
Networks
Overview
e
Ht
η
Ht+∆t P
P e
Lt
λ
L t+∆t
Micro-foundation Reconstructing high-level structure from low-level dynamics: — reverse problem: find λ such that P ◦ λ = η e ◦ P.
Framework and objectives
Epistemic communities
Micro-foundations
Networks
Overview
e
Ht
η
P
P Lt
Ht+∆t
λ
L t+∆t
Micro-foundation Reconstructing high-level structure from low-level dynamics: — reverse problem: find λ such that P ◦ λ = η e ◦ P.
Framework and objectives
Epistemic communities
Micro-foundations
Networks
Epistemic networks Definitions What is an epistemic network? A network of agents: S=(S, ES ), evolving with time: S(t) Semantic network: network of concepts, C=(C, EC ) Agents are linked to concepts they use, through R. Three kinds of relations: RS , RC and R: s’
C
c’ c
s s" S
c"
Framework and objectives
Epistemic communities
Micro-foundations
Networks
Epistemic networks Definitions What is an epistemic network? A network of agents: S=(S, ES ), evolving with time: S(t) Semantic network: network of concepts, C=(C, EC ) Agents are linked to concepts they use, through R. Three kinds of relations: RS , RC and R: s’
C
c’ c
s s" S
c"
Framework and objectives
Epistemic communities
Micro-foundations
Networks
Epistemic networks Definitions What is an epistemic network? A network of agents: S=(S, ES ), evolving with time: S(t) Semantic network: network of concepts, C=(C, EC ) Agents are linked to concepts they use, through R. Three kinds of relations: RS , RC and R: s’
C
c’ c
s s" S
c"
Framework and objectives
Epistemic communities
Micro-foundations
Networks
Network morphogenesis
A brief survey 1
Early times: Erdos-Renyi, until unsatisfying power-law degree distribution and other statistical parameters
2
Pioneering models rebuild clustering, and degree distribution (preferential attachment (PA), network growth)
3
Since then and until now: models introducing various kinds of PA to rebuild diverse statistical parameters
4
But even with credible hypotheses, rare empirical validations, yet needed for realistic morphogenesis models
Framework and objectives
Epistemic communities
Micro-foundations
Networks
Network morphogenesis
A brief survey 1
Early times: Erdos-Renyi, until unsatisfying power-law degree distribution and other statistical parameters
2
Pioneering models rebuild clustering, and degree distribution (preferential attachment (PA), network growth)
3
Since then and until now: models introducing various kinds of PA to rebuild diverse statistical parameters
4
But even with credible hypotheses, rare empirical validations, yet needed for realistic morphogenesis models
Framework and objectives
Epistemic communities
Micro-foundations
Towards a rebuilding model
High-level features Degree distributions Four degree distributions: social, semantic, socio-semantic (from agents, from concepts) Power-law tail, log-normal fit Clustering structure High clustering both for monopartite coefficients and bipartite coefficients Epistemic community structure Many large ECs, particular distribution of EC sizes.
Framework and objectives
Epistemic communities
Micro-foundations
Towards a rebuilding model
Suggest empirically credible low-level dynamics Measuring interaction behavior Measure the interaction behavior of agents Have an essential preference f for nodes of kind m: P(L|m) ν(m) → we may estimate f through ˆf (m) = P(m) Check correlations between parameters: cˆm0 (m) = Event-based modeling Distinguish activity from attractivity: rich-get-richer or rich-work-harder? Activity and interactivity: f (m) = a(m)ι(m)
P(m|m0 ) P(m)
Framework and objectives
Epistemic communities
Micro-foundations
Towards a rebuilding model
Suggest empirically credible low-level dynamics Measuring interaction behavior Measure the interaction behavior of agents Have an essential preference f for nodes of kind m: P(L|m) ν(m) → we may estimate f through ˆf (m) = P(m) Check correlations between parameters: cˆm0 (m) = Event-based modeling Distinguish activity from attractivity: rich-get-richer or rich-work-harder? Activity and interactivity: f (m) = a(m)ι(m)
P(m|m0 ) P(m)
Framework and objectives
Epistemic communities
Micro-foundations
Towards a rebuilding model
Measuring low-level dynamics
Network growth Event-based low-level dynamics Choice of agents Geometric distribution of agents, tri-modal distribution for newbies Choice of concepts Geometric distribution of concepts, uni-modal distribution of novel concepts
Framework and objectives
Epistemic communities
Micro-foundations
Reconstruction of epistemic communities
Model design At (i) 1 St(i)
Ct (i)
2
ν
ν
Ct (i)
St(i)
St(i)
new agents
3 initiator (~P(k))
St(i)
recruitment of other agents ~P(k,d)
concept set of old agents ν St(i) \ St(i)
4
selection ~P(k concepts−>agents)
St(i)
Ct (i) ν
St(i)
ν
Ct (i)
Framework and objectives
Epistemic communities
Micro-foundations
Reconstruction of epistemic communities
Reconstruction Epistemic communities are produced by the co-evolution of agents and concepts number of ECs
Degree distributions, clustering structure, epistemic structure are reconstructed.
1000
100
10
1
0.1 EC size 10
20
30
40
50
60
70
80
90 100 110 120 130 140 150 160 170
Reconstruct high-level statistical parameters meaningful for epistemic networks Respecting low-level dynamics: descriptive rather than normative
Framework and objectives
Epistemic communities
Micro-foundations
Reconstruction of epistemic communities
Reconstruction Epistemic communities are produced by the co-evolution of agents and concepts number of ECs
Degree distributions, clustering structure, epistemic structure are reconstructed.
1000
100
10
1
0.1 EC size 10
20
30
40
50
60
70
80
90 100 110 120 130 140 150 160 170
Reconstruct high-level statistical parameters meaningful for epistemic networks Respecting low-level dynamics: descriptive rather than normative
Framework and objectives
Epistemic communities
Micro-foundations
Conclusion
e
Ht
η
P
P Lt
Ht+∆t
λ
L t+∆t
Integrated example of reconstruction in social science preliminary to studying knowledge diffusion and, eventually, naturalizing cultural anthropology
Framework and objectives
Epistemic communities
Micro-foundations
Conclusion
e
Ht
η
P
P Lt
Ht+∆t
λ
L t+∆t
Integrated example of reconstruction in social science preliminary to studying knowledge diffusion and, eventually, naturalizing cultural anthropology
Framework and objectives
Epistemic communities
Micro-foundations
Conclusion
e
Ht
η
P
P Lt
Ht+∆t
λ
L t+∆t
Integrated example of reconstruction in social science preliminary to studying knowledge diffusion and, eventually, naturalizing cultural anthropology
Framework and objectives
Epistemic communities
Micro-foundations
Framework and objectives
Epistemic communities
Micro-foundations
Appraising levels Relationships between different levels Dualism, reductionism ? Emergentism: low-level phenomena cause high-level phenomena, yet in turn not necessarily reduceable to low-level phenomena. Is it ok that a lower level creates a higher level, then the higher level in turn influences the lower level? Rather, different modes of access to a same process: dual-mode of operational access. “There may be emergence without emergent properties. Not asymmetric emergence of high-level properties out of basic properties, but symmetrical co-emergence of microscopic low-level features and high level behavior” (Bitbol, 2005)
Framework and objectives
Epistemic communities
Micro-foundations
Appraising levels Relationships between different levels Dualism, reductionism ? Emergentism: low-level phenomena cause high-level phenomena, yet in turn not necessarily reduceable to low-level phenomena. Is it ok that a lower level creates a higher level, then the higher level in turn influences the lower level? Rather, different modes of access to a same process: dual-mode of operational access. “There may be emergence without emergent properties. Not asymmetric emergence of high-level properties out of basic properties, but symmetrical co-emergence of microscopic low-level features and high level behavior” (Bitbol, 2005)
Framework and objectives
Epistemic communities
Micro-foundations
Appraising levels Relationships between different levels Dualism, reductionism ? Emergentism: low-level phenomena cause high-level phenomena, yet in turn not necessarily reduceable to low-level phenomena. Is it ok that a lower level creates a higher level, then the higher level in turn influences the lower level? Rather, different modes of access to a same process: dual-mode of operational access. “There may be emergence without emergent properties. Not asymmetric emergence of high-level properties out of basic properties, but symmetrical co-emergence of microscopic low-level features and high level behavior” (Bitbol, 2005)
Framework and objectives
Epistemic communities
Micro-foundations
Appraising levels Relationships between different levels Dualism, reductionism ? Emergentism: low-level phenomena cause high-level phenomena, yet in turn not necessarily reduceable to low-level phenomena. Is it ok that a lower level creates a higher level, then the higher level in turn influences the lower level? Rather, different modes of access to a same process: dual-mode of operational access. “There may be emergence without emergent properties. Not asymmetric emergence of high-level properties out of basic properties, but symmetrical co-emergence of microscopic low-level features and high level behavior” (Bitbol, 2005)
Framework and objectives
Epistemic communities
Micro-foundations
Levels as observations
Each level is an observation instrument (a phenomenon), and may provide information about some other observation gained through other instruments.
Framework and objectives
Epistemic communities
Micro-foundations
Levels as observations
Each level is an observation instrument (a phenomenon), and may provide information about some other observation gained through other instruments. “Observationism” 1
no substantial reality of levels
2
no reciprocal causation, but informational links
3
some phenomena cannot be rebuild from some given lower-level decriptions
Framework and objectives
Epistemic communities
Micro-foundations
Modeling links between levels
Reconstruction “Observationism” induces simply informational dependence between both levels: λ(L|H), η(L|H) Thus, reconstruction failure may also come from ill-defined levels: not yielding enough information about the given phenomenon (e.g. learning & glial cells; concepts in addition to simple social interactions between agents) Reductionism only works when H is fully deduceable, not reduceable, from L.
Framework and objectives
Epistemic communities
Micro-foundations
Modeling links between levels
Reconstruction “Observationism” induces simply informational dependence between both levels: λ(L|H), η(L|H) Thus, reconstruction failure may also come from ill-defined levels: not yielding enough information about the given phenomenon (e.g. learning & glial cells; concepts in addition to simple social interactions between agents) Reductionism only works when H is fully deduceable, not reduceable, from L.
Framework and objectives
Epistemic communities
Micro-foundations
Stigmergence
Co-evolutionary framework Additionally, this viewpoint is not contradictory with some sort of causal retroaction: action of a group of neurons onto another group of neurons, agents creating & modifying their environment which in turn “acts upon them”: stigmergence. No downward causation either, simply influence of already existing environmental artifacts In our case, there is a co-evolution between semantic and social networks.
Framework and objectives
Epistemic communities
Micro-foundations
Stigmergence
Co-evolutionary framework Additionally, this viewpoint is not contradictory with some sort of causal retroaction: action of a group of neurons onto another group of neurons, agents creating & modifying their environment which in turn “acts upon them”: stigmergence. No downward causation either, simply influence of already existing environmental artifacts In our case, there is a co-evolution between semantic and social networks.
